On Monday, I published the story of Tommy Pickett, a resident of Fulham's West Kensington estate in the Conservative flagship borough of Hammersmith and Fulham (H&F). Tommy described being visited by a man who said he was campaigning for Boris Johnson and told him that if he backed H&F's controversial plan to demolish the estate and its neighbour Gibbs Green he would be "picked first" for a replacement home in a new development in nearby Seagrave Road.

The particular significance of this is that the plan for the Seagrave Road site includes only the first 200 of a promised 760 homes that would replace those of the two estates within a proposed redevelopment of the wider area, known as the Earls Court project – an ambitious, 77-acre enterprise that H&F's developer partner Capco estimates could eventually be worth £8 billion.

The advantage of being included on any so-called "early movers list" or "VIP list" relating to Seagrave Road – the council denies that one exists - is that those on it would be settled in their new homes away from the estates before their destruction and any ensuing new building began. In other words, they wouldn't have to live in the middle of a demolition or construction site for years, maybe many of them.

Tommy doesn't know the identity of the man who came to see him, but understood him to be "from the council" in some way, and therefore an authority on the demolition issue. He says he took the man's advice to immediately respond to the council's formal consultation of residents by expressing support for the proposed demolition and sending off his form the following day.

Last month, the Metropolitan Police were supplied with a document containing what was described as evidence supporting allegations that "public officers" had promised preferential treatment in the allocation of new homes in Seagrave Road to some residents of the estates in exchange for their supporting the proposed demolition.

I understand that Scotland Yard detectives are still assessing the material, which sets out an argument that the law may have been broken. Whatever the police's conclusion, it is apparent that Tommy Pickett is not the only resident of the West Kensington estate with the clear impression of being told by someone working on the Earls Court project that they can be confident of securing one of those first 200 replacement homes.

Elsie Webb, 65, who was born in Newcastle but has lived in Desborough House on the West Kensington estate in a two-bedroom flat with her son since 1983, and had previously lived for eight years in a different part of the estate, recalls attending a meeting about the future of the two estates at the Gibbs Green community centre, which she says took place "about two years ago." She named two officers of Hammersmith and Fulham council who were at the meeting and answering questions from residents. Elsie recounts asking one of the officers a question in relation to the homes planned for Seagrave Road:

I put my hand up and I said, "I've got a difficulty here, I've got my son living with me and he's far too old to be living with me, he's 36 now." I said, "Is there a possibility that you could give us two one-bedroom flats?" "Definitely," he says. I thought, oh, fantastic. That made me feel a bit better.

Elsie doesn't want to lose the flat she lives in at present and confirmed that she'd asked her question knowing that it might be demolished anyway. But if she were forced to move, she explained, it would be a consolation if her son, a working man whose earnings she indicated are too low to meet rents in the local private rented sector, got a council flat to himself at long last. She describes him as "absolutely desperate" to have his own place.

I asked Elsie if she was quite sure that the council officer who answered her question was referring specifically to Seagrave Road, rather than the wider Earls Court project redevelopment area. She said she was certain that this was the case:

[The officer] was talking about moving us to Seagrave Road. Cos I thought, here's my son's chance…this would be a chance to get him housed.

I twice invited Elsie to sum up the position as she saw it. After all, the officer might have simply handled her question badly. Perhaps a misunderstanding had occurred. Elsie herself described what the officer said as "a burble promise," and says she isn't certain that it will be kept. So was she quite clear in her mind that she'd been told by an officer of H&F that she would definitely – not just possibly - be allocated at least one of the new homes in the Seagrave Road development? "Yes," she replied and then, "Absolutely."

Unlike Tommy Pickett, Elsie does not say that she was told she would receive priority treatment in the allocation of Seagrave Road homes if she quickly expressed support for the demolition of the West Kensington and Gibbs Green estates. She does, though, say that she firmly believes she has been told that two of the first 200 replacements for the 760 homes that will be demolished should the full Earls Court project go ahead will be given to her and her son.

What if things don't work out that way? What if the council officer made an irresponsible commitment that won't be honoured? "If this is fictitious, I'm definitely just going to stay here," Elsie said. "I think I'll campaign, try and put letters through everybody's door, saying, 'You don't know where you're going now. If the council comes [to move you], say no!' Have a sit-in. Say, 'I'm not going anywhere.' Because, why should we be moved?

There's nothing wrong with this building, it's perfectly sound structurally, and it's kept reasonably clean, you know, the lifts and the corridors, you don't see any mess there. I don't see anything wrong. Now, they're saying this is slummy. Can you see anything slummy? I can't. And this estate has been quite safe, I have never had a day's trouble. I used to go out dancing in my forties and fifties, and I'd walk up the road, two, three o'clock in the morning, absolutely not worried one bit."

Hammersmith and Fulham has previously stated that it has not compiled an "early leavers list" or "VIP list" of estate residents to be given preferential treatment, and says will all be treated equally under a local lettings plan. However, the council's chief executive has said in correspondence with the leader of its opposition Labour group, Stephen Cowan, that he is "satisfied" that although council officers have not been involved, others with an interest in the estates being demolished did compile a list of residents favouring this course.

I've invited the council to comment on the allegations contained in the report handed to the police and on what Elsie Webb has said in this article. I will add as an update any response that they provide.

Comments are not open on this article but readers wishing to respond to it can email me at dave.hill@guardian.co.uk